2017/12/23 by Evgenios T. A. Kakariadis, Kakariadis, Evgenios T. A.
Physics and Astronomy · #46L08 #46L30 #46L55 #58B34 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Quantum Mechanics and Applications #Quantum chaos and dynamical systems #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.1712.08795
openalex publication_date 2017/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider Pimsner algebras that arise from C*-correspondences of finite\nrank, as dynamical systems with their rotational action. We revisit the\nLaca-Neshveyev classification of their equilibrium states at positive inverse\ntemperature along with the parametrizations of the finite and the infinite\nparts simplices by tracial states on the diagonal. The finite rank entails an\nentropy theory that shapes the KMS-structure. We prove that the infimum of the\ntracial entropies dictates the critical inverse temperature, below which there\nare no equilibrium states for all Pimsner algebras. We view the latter as the\nentropy of the ambient C*-correspondence. This may differ from what we call\nstrong entropy, above which there are no equilibrium states of infinite type.\nIn particular, when the diagonal is abelian then the strong entropy is a\nmaximum critical temperature for those. In this sense we complete the\nparametrization method of Laca-Raeburn and unify a number of examples in the\nliterature.\n